1 Introduction IN THE early days of electrical engineering there were anecdotal reports of sensations perceived by power-house workers who came close to transformers carrying high alternating currents. It was suspected that the strong alternating magnetic fields surrounding these transformers caused stimulation of excitable tissues within the body. The confirmatory experiment was performed by D'ARSONVAL (1896) who placed the head of a subject in a large coil carrying 32A at 42Hz. The subject reported seeing phosphenes, i.e. bright spots in the visual field, indicating stimulation of tissues of the optical pathway. Since then there have been many studies of eddy-current stimulation of the retina and motor and sensory nerves (GEDDES, 1989). Magnetic stimulation of the nervous system has proven to be less painful than stimulation by current injected through electrodes in direct contact. This fact was demonstrated by BARKER et al. (1985) when stimulating the human cortex. In recent studies there has been concern about accidental stimulation of the heart by magnetic fields. Two studies (RENTSCH, 1965; IRWIN et al., 1970) failed to achieve cardiac stimulation with pulsed magnetic fields. Cardiac arrhythmias were observed in dogs (SILNY, 1985) subjected to a single cycle of a 50Hz, 2T magnetic field generated by Helmholtz coils. The ECG shown by SILNY reveals events consistent with stimulation of parasympathetic nerves innervating the heart. In addition, Correspondence should be addressed to Dr Joe D. Bourland, Hillenbrand Biomedical Engineering Center, Potter Engineering Center, Purdue University, W. Lafayette, IN 47907, USA. First received 4th June 1990 and in final form l Oth April 1991
9 IFMBE: 1992
162
therapeutic devices employing magnetic fields to stimulate the heart without undue pain are contemplated. In a technical note, we (BoURLAND et al., 1990) reported excitation of the canine heart with a pulsed magnetic field produced by discharging a capacitor bank into a coil placed on the chest. The present l 1-dog study reports the threshold excitation-coil current and energy and the induced electric field strength required to excite the canine ventricles with two coplanar coils applied to the chest. 2 Theory 2.1 Conventional stimulation For excitable tissue to be stimulated, it is necessary to remove a critical amount of charge from the cell membrane. Removal of this charge reduces the resting membrane potential (RMP) by AV to the threshold potential (TP), at which point a regenerative process occurs with an opening of ion channels and a transmembrane movement of sodium and potassium ions, thereby generating an action potential. This process is illustrated for the cardiac muscle by the inset in Fig. 1. To achieve the initial reduction in transmembrane potential (AV), the stimulating current must establish a critical current density at the cell membrane for a finite time. The excitability characteristic of a tissue is described by the strength/duration curve, which is a plot of the threshold current against the pulse duration, d. There are two expressions for the strength/duration curve: the empirical LAPICQUE (1909; 1926) and the BLAIR (1932), which was derived using membrane theory. AVERS et al. (1986) and MOUCHAWAR et al. 0989) have shown that experimentally
M e d i c a l & Biological Engineering & Computing
March 1992
obtained data fit both expressions reasonably well. As the Blair expression was derived using the properties of the cell membrane, it will be used in the present study. However, the c o m m o n feature of both strength/duration expressions is that the shorter the duration of the current pulse, the higher the current required for stimulation. Fig. 1 shows strength/duration curves for the m o t o r nerve,
electric charge and A is the magnetic vector potential, the source of which is electric current (moving electric charge). In magnetic stimulation, the current in the excitation coil gives rise to an induced current density in the tissue. The electrical skin depth is 6, given by
1 =
(3)
2000l~
1~176176 \
\
200L -,,, \ -
where f is the frequency, /~ is the magnetic permeability and a is the tissue conductivity 9 Skin depth is a measure of the distance over which the applied AC magnetic field is attenuated by the induced eddy current. A typical equivalent frequency in magnetic stimulation is 10kHz, the permeability of tissue is nearly equal to the free space value of 4n x 10 7 H m - X and the conductivity is approximately 1 S m - 1. Therefore, the skin depth in the tissue is
0
100-. \,, ~ "'.. "\\ ~ j 50 -'".. \Xx ~ "'... "X ~ Jb 20 "'"-. "'x ~ \\ \ -
TP _ _~_]__ __\ RMP~ M..._.. stimulus
-Nd~
9.,.,,
I0
.... \\x\ "% "".,. ,,. \XX\ ~
5
0
0'001
L
0'01
1 (~tlssue
,
a
0.1
I
I
'0
'
I00
duration,ms
Fig. 1 Strength/duration curves for motor nerve, sensory receptors and cardiac muscle. For ease of comparison, the curves have been normalised to the same rheobase. Inset shows the mechanism of stimulation. [ T P = threshold potential, R M P = resting membrane potential, d = duration, (J/Jb) = (1/1 e-a/~)] heart z = 2 ms sensory receptors z = 0"5 ms ....... motor nerve z = 0.1 ms -
=
~/(~)(lO*)(4~z x 10-7)(1)
=
5m
Typically, the distance between the coil and the target tissue is a few cm, much less than 6ti.... . Consequently, the contribution of the eddy-current in the tissue to the induced electric field can be neglected in calculating the vector potential. At a point r in the tissue, the vector potential A is obtained by integrating over the current in the coil A(r) =
/to f Jcoit(r') d V '
(4)
-
sensory receptors and cardiac muscle. The current is represented as current density J divided by the rheobasic current, density Jb- The rheobase is the long-duration current asymptote. The Blair expression for the strength/duration curve in terms of current density J is Jb J - (1 - e -d/r (1) where Jb is the rheobase and z is the membrane time constant, a quantity that is specific for each type of tissue; z is also temperature dependent (GEDDES and BOURLAND, 1985). The membrane time constant is the duration for which J / J b = 1"58. Fig. 1 shows that with a stimulus of 0.1 ms, the threshold for stimulating the m o t o r nerve (z --~ 0.1 ms) is 1.58 Jb" However, if the same pulse duration is used to stimulate the heart (z ~ 2 ms), the current density must be 20-5 times the rheobase or 13 times that required to stimulate the m o t o r nerve. Therefore, for stimulating cardiac muscle, a longer pulse duration is desirable. With a rectangular pulse, the average rheobasic current density for cardiac muscle is 1 . 4 8 m A c m 1 (PEARCE et al., 1982) and the resistivity is approximately 4 0 0 D c m (GEDDES and BAKER, 1989). Therefore, the expected rheobasic electric field strength is E b = PJb = 5 9 2 m V c m 1 ~ 6 0 V m - ~ . 2.2 Eddy-current stimulation With magnetic (eddy-current) stimulation, the induced electric field E causes current to flow in the tissue, thereby causing stimulation. The current density J is E/p, where p is the resistivity of the tissue. In a stationary system, the electric field E is given by OA E = - - V ( I ) - c~--t-
(2)
where (I) is the electrostatic potential that arises from fixed Medical & Biological Engineering & C o m p u t i n g
where 2cou(r' ) is the current density at point r' in the coil, /~o is the permeability of free space and dV' is an element of volume. The electrostatic potential at point r is given by
*(,.)
=
["
4Xeo J Ir - r'l
dV'
(5)
where r is the electric charge density at point r', eo is the permittivity of free space, dV' is an element of volume and the integral is taken over all space. It can be shown using Maxwell's equations that there is no electric charge due to a time-varying electric field within a linear dielectric of uniform electrical properties. The primary origin of V~ in magnetic stimulation is the electrical charges that accumulate at the interfaces between regions of different conductivity in the tissue and at the air/skin interface of the subject. For typical tissues and stimulation waveforms, the dielectric relaxation time e/a is small compared to the period of the stimulating current pulse. The charges at the interface can then be calculated from the resulting requirement that the normal component of the current density is continuous at an interface between different conductors. 2.3 Predicted energy f o r cardiac stimulation Using the Blair expression we can demonstrate how the energy delivered to the coils varies with pulse duration for stimulation with a pulsed magnetic field. With the electric field E = p J as the stimulus, the Blair expression is Eb
E--(l_e
d/,)
(6)
where Eb is the rheobasic electric field and ~ is the membrane time constant. The induced electric field E is proportional to the first time derivative of the coil current di/dt. To generate an idealised rectangular pulse of electrical field E in the tissue, the current in the coil must be a rising r a m p with a constant time derivative of K E , where
M a r c h 1992
163
K is a constant of proportionality that depends on coil geometry and coil-to-tissue distance. The peak magnetic field energy UB delivered to the coils is given by 1 2 UB = -iLIp
(7)
where L is the coil inductance and Ip is the peak current in the coil. If the ramp is used for the coil current waveform, Ip is equal to KEd, where d is the duration to the peak of the current ramp (and is also the duration of the induced rectangular electric field pulse). Therefore, K2 U . = - ~ L(Ed) 2
(8)
Substituting the expression for E from the strength/ duration curve into the preceding equation we obtain Kz E~ UB = -~- L (1 -- e-d/q 2 d2
(9)
For the simple geometry of small coils parallel to the tissue surface, the tissue can be modelled as an infinite conductive half-space. For this case, the constant K can be shown to be numerically equal to 1/A o, where A 0 is the magnitude of the magnetic vector potential (eqn. 4) evaluated at the target tissue depth for 1 A of current in the stimulating coil assembly (NYENHU]S et al., 1991). The value of A 0, obtained from a computer model of the two-coil assembly used for cardiac stimulation, was 7-6 • 10 -6 V s A - 1 m - ~. Evaluating A o by computer simulation for a coil-to-tissue distance of 2-5cm and for the coils shown in Fig. 2, the predicted magnetic field energy against pulse duration required to stimulate the dog heart (z ~ 2 ms) can be calculated as a function of pulse duration. As shown in Fig. 2, the magnetic field energy decreases monotonically as duration decreases. The magnetic field energy approaches a minimum asymptotically as the duration of the pulse approaches zero. To find the minimum, we can use the Taylor series expansion for the exponential e -d/~. Neglecting the higher-than-linear terms, the expansion becomes 1 - (d/z), for d ~ z. The minimum energy is therefore L
L E~ dZ = ~ o
(10)
E~z 2
If we use J b = 1.48mAcro 2 and p = 4 0 0 f 2 c m , the expected rheobasic electric field strength is E b ~ 60 V m-~ and the minimum predicted energy for cardiac stimulation is U~,~.--27kJ. As a practical matter, the rapid rate of flux change required for minimum energy stimulation exceeds the practical construction technique and electronic 200
_~ 16o
device specifications, and so a compromise between minimum energy and device limitations must be achieved. Based on our experience with high-energy defibrillators designed and constructed for research, we chose to limit the capacitor-bank voltage to 10000V; the predicted threshold energy is approximately 36 kJ and the duration of the generated pulse is approximately 600/zs. The magnetic stimulator used in this study was designed to induced a 571/zs pulse in the tissue. 2.4 Magnetically-induced stimulus waveform As shown in Section 2.3, the energy required for magnetic stimulation of the heart is large. A typical magnetic stimulator includes an energy-storage capacitor, which is discharged into an excitation coil. F r o m Faraday's law of induction, the waveform of the current density (J) induced in the tissue is proportional to the first time derivative (dic/dt) of the current (ic) in the excitation coil. WESSALEet al. (1980) and BOURLAND et al. (1978a; b) have shown that trapezoidal and damped sine waves are equally effective if they have the same average current. This provides a convenient way to relate the peak value of the induced field to its efficacy. (The peak and average values are the same for a rectangular pulse.) When a capacitor C, charged to V V, is discharged into an excitation coil of inductance L and circuit resistance R, the current in the coil is a damped sinusoid. With a typical magnetic stimulator, the damping D = (R/2)x/(C/L) is less than 1.0 and the excitation coil current (ic) waveform is oscillatory and is given by V i~ = - ~ e -~t sin cot
(11)
where ~ = R / 2 L and co = x / ( 1 / L C ) - ~2 (GEDDES and BAKER, 1989). A resistor and series diode were placed in parallel with the energy-storage capacitors of the generator used in this study to prevent significant reverse voltage developing across the (electrolytic) energy-storage capacitors. A similar circuit configuration was used by BARKER et al. (1985). The resistor-diode network increases the decay time constant after the peak in coil current and the reverse current density induced in the tissue is attenuated and prolonged. Consequently, stimulation is caused by the portion of the waveform from the time of onset (t = 0) to the time of peak coil current (t = Zp). (The diode of the added circuitry is reverse-biased during this time, 0 ~< t ~< zp, and the additional circuitry has no effect on the coil current and the induced current density.) Let F be the ratio of the average induced current density (Jav) to peak induced current density (Je) in the time 0 ~< t ~< rp, i.e. I" = (JAv/Jp). Assuming that the tissue is a linear conductor, the induced current density is proportional to the first time derivative of the coil current. Noting also that the peak of the induced current occurs at t -- 0, then
o
120
F = zv J~ ._u
dt dt =
ic(t = Zv)
dic (t = O)
80
di~
at
O
(t
(12)
= o)
Using the preceding expressions for i~ and noting that (di~/dt) (t = O)= (V/L), we obtain the following for the underdamped circuit. 0 I
o.oi
' o.1o
' 1.oo
1o.'0 o
Underdamped case: D < 1
durolion.ms Fig. 2
164
Predicted energy required against stimulus duration for stimulating cardiac muscle with a pulsed magnetic field
z,
=
-- tan-1 fO
=
-- tan-1 fO
Medical & Biological Engineering & Computing
(13) March 1992
where 7 = ~/o9 = (D/~/1 - D 2 ) . The average-to-peak ratio for the induced current can be calculated as a function of damping from e - ' 'a"-'(1/y) sin ( t a n - 1 ~) F =
(14) tan- 1 1 7
and Welfare (DHHS publication NIH 85-23, revised 1985). In addition, this study was approved by the Purdue University Animal Care and Use Committee. Ectopic beats were produced in the vagal-arrested hearts of 11 male and female mongrel dogs, with body weights from 17 to 26kgl The dogs were anaesthetised with IV pentobarbital sodium (30mgkg-l), intubated, ventilated with room air and placed in left lateral recumbency. The coplanar coils were placed beneath the dog, with the heart
Similarly, the following expressions for F in the critically damped (D = 1.0) and overdamped cases (D > 1.0) can be obtained. Critically damped case: D = 1 F-
1 (15)
e
o 8.5cm
Overdamped case: D > 1
expl--89 F=
-- 1) In 7 + 11] - exp[- 89 7-7+1 In m 7-1
+ 1) In 7 + 11] Y-
(16)
~
~ B1
where D
,
L
~
~~
~
.
~
~
1.25cm
7 -- , , / D 2 _ 1 "
Fig. 3 shows the ratio of the average-to-peak induced current against the damping coefficient (D) for the range 0-1.5. This illustration shows that it is desirable to select a
01
I
lay
o, O.
r-
04,
0.2
o
o'.5
~io
1!5
damping,D
Fig. 3
Fig. 4
(a) Position o f the coplanar coils (broken circles) under the left side o f the dog; (b) dimensions and current f l o w in the coils
above the point where the perimeters of the coils touched, as shown in Fig. 4. Lead II electrocardiogram and the direct arterial pressure were recorded. A bipolar stimulating electrode was placed inside an insulating sleeve and in contact with the right vagus nerve in the neck. Reversible and temporary cardiac arrest was achieved by stimulating the right vagus nerve with a train of rectangular pulses, 0.1 ms in duration at 50s 1 and approximately 15 V, using a Grass $44 stimulator and SIU5 isolation unit (Grass Instrumentations, Quincy, MA, USA). Prior to delivering magnetic pulses, and at selected times throughout the procedure, the vagus nerve was stimulated and magnetic pulses were not delivered to verify that latent cardiac pacemakers were silent.
Ip
0.8
B2
Ratio F of the average-to-peak value of induced current/ density pulse in the time between the onset (t = O) of the pulse and the time (t = zp) of the zero crossing of the pulse as a function of damping D
low damping to obtain a high average current. The damping coefficient for the stimulator used in this study was D = 0.105, and the peak induced field can be related to that for a rectangular pulse by multiplying by 0.581. 3 M e t h o d s and m a t e r i a l s
3.1 Animal preparation All experiments were performed in accordance with the Guide for the Care and Use of Laboratory Animals, published by the US Department of Health, Education Medical & Biological Engineering & Computing
3.2 Excitation coils Two coplanar coils (Fig. 4) provided the pulsed magnetic field. This arrangement concentrates the induced electrical field in the region where the coils are adjacent when the coils are connected so that current flows in the same direction at the point of contact (Fig. 4b) (UENO et al., 1988). NYENHUIS et al. (1991) have shown that the use of two coplanar coils, instead of one coil of the same dimensions, results in the reduction of almost a factor of two in the energy required to achieve stimulation. Each coil consisted of 30 turns of 0.5in x 0.043in of copper ribbon covered with braided glass sleeving and sealed with epoxy cement. The inner and outer diameters of each coil were 7 and 17cm, respectively. The coils were mounted with their edges touching. This geometry provides optimum stimulation of a target 2.5 cm from the adjacent coil edges (NYENHUIS e t al., 1991). The distance between the plane of the coil and the heart
March 1992
165
was measured by inserting the hypodermic needle through the intercostal space where the coils touched. The needle was advanced until cardiac motion was felt through the needle, or until ectopic beats were provoked by the sharp needle point. In these studies the distance from the coils to the ventricles within the chest ranged from 2 to 3-5 cm. 3.3 Magnetic stimulator A simplified equivalent circuit of the magnetic stimulator and coils is a series R C L circuit, comprising a 682 #F 9 9 0 0 V capacitor, an output switch (ignitron) and a 220 m H inductor (combined value for both coils, including mutual inductance). In addition, a 220ml) resistance and reverse-biase diode is connected across the 682#F capacitor to prevent reverse polarisation. A similar circuit was described by BARKER et al. (1985) for stimulation of the h u m a n brain. Delivery of the current was initiated by triggering a General Electric GL7171 ignitron. The equivalent internal series resistance of the generator is approximately
3
vagal stimulation
"o
0
0
2
4
6
8
10
time,s G -1-
85 m~); the series resistance of the two coils and connecting leads is approximately 35 m~). The generator specifications are: m a x i m u m voltage 9900V, m a x i m u m peak current 17000A and maximum stored energy 33 400J. Surge line current was limited to 13 A (at 115 V) so that the magnetic stimulator could be powered from any standard outlet in the laboratory; maximum line current is required only during charging of the energy-storage capacitors. Full charge is achieved in approximately 90 s. The waveform of the electric field induced in the tissue by the magnetic stimulator used in this study is shown in the inset of Fig. 3. The damping D = 0-105 and the duration to the first zero crossing of the induced current is zp = 571#s. 3.4 Threshold stimulus determination The procedure used to determine the threshold current and energy required to evoke a cardiac contraction was as follows: The capacitor bank was charged to a selected voltage. The right vagus nerve was stimulated to temporarily arrest the heart. After sufficient time to verify cardiac arrest, typically about 3 s, a test pulse was delivered while monitoring the ECG and blood pressure recordings. If an ectopic beat was produced, the capacitor-bank voltage was reduced by decrements of l0 per cent until the pulsed magnetic field failed to evoke a ventricular contraction. Otherwise, the capacitor-bank voltage was increased by increments of 10 per cent until an ectopic beat was produced. The threshold was defined as that voltage (and current) for which 10 per cent less did not stimulate. For each trial, the heart was arrested for about 5s. The procedure was repeated to obtain a threshold with current flowing in the opposite direction in the pair of coils.
E 200
E :3
160
& ~20 13 0
o
80
.13
~L.
40
mognetic pulse delivered
l
L, 0
i
i
2
4
i
i
6
8
time, s b
Fig. 5
(a) ECG; (b) blood pressure, before cardiac arrest, during cardiac arrest of the heart and after cessation of vagal stimulation. During cardiac arrest the magnetic stimulator evoked an ectopic beat, shown by the QS-wave and the blood-pressure pulse P Table 1
166
4 Results Fig. 5 is a typical recording of the E C G and blood pressure prior to cardiac arrest, during arrest with vagal stimulation when an ectopic beat was induced by the magnetic stimulator and following cessation of vagal stimulation when the heart resumed normal sinus rhythm. Note that during the period of cardiac arrest, the ectopic beat induced by the pulsed magnetic field provided an inverted (QS) waveform in the ECG, indicating apical stimulation of the ventricles. The mean threshold stimulating current in the excitation coils was about 9250A. Table 1 presents the threshold peak currents and energies for current flow in directions A and B. Direction A was defined as anticlockwise current in the cranial coil and clockwise in the caudal coil, when
Threshold current and energy delivery to the excitation coil
Dog number
Current Direction A (A)
Current Direction B (A)
Stored energy Direction A (J)
Stored energy Direction B (J)
Average stored energy (J)
Energy ratio A/B
Induced E field Vm '
1 2 3 4 5 6 7 8 9 10 11
8600 9200 8000 8800 9400 8800 10000 10200 9600 10600 8800
8500 10200 8800 8000 9400 8800 10000 9400 9200 9400 9600
9385 12258 8513 10300 12258 10300 14386 14386 12258 15285 11454
9385 14386 10300 8513 12258 10300 14386 12258 12258 12258 13514
9385 13322 9407 9407 12258 10300 14386 13322 12258 13772 12484
1.0 0.85 0-83 1.21 1.0 1.0 1.0 1.17 1.0 1.25 0-85
213 230 227 207 182 205 212 216 196 216 237
Mean SD
9273 776
9209 646
11889 2175
11801 1957
11846 1887
1.01 0-14
213 16
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M a r c h 1992
viewed from above. Direction B is the reverse. The average threshold for inducing an ectopic beat was slightly greater with current flow in direction A than B, but the difference was not significant at p = 0.05.
5 Discussion In this paper, we have presented both theoretical predictions and experimental data for cardiac threshold. The theoretical predictions were based on a simplified model of the experimental subject, and were not expected to be in quantitative agreement with the experimentally determined values for cardiac threshold, but rather, were used to optimise the design of the hardware. We anticipated, as had others, that the energy required for cardiac stimulation would be considerable, and we desired to reduce the size and power of the pulse generator as much as possible, by optimising the design for minimum energy. An average energy of approximately 12kJ was required to achieve closed-chest magnetically induced ectopic beats in the 17-26 kg dogs. The energy required to stimulate the heart is much greater than that reported for superficial motor nerves (BICKFORD and FREMMING, 1965; POLSON et al., 1982), but is considerably less than the 20-105kJ suggested by IRWIN et al. (1970). The energy required to stimulate the heart is more than an order of magnitude higher than the energy required to stimulate the human brain and peripheral nervous system (typically 400 J). If it is assumed that the charge accumulated at boundaries between tissues with differing resistivity is insignificant, the mean peak induced electric field for threshold stimulation in the dog was 2 1 3 V m -1 for the 571kts damped sine wave pulse. Using the Blair expression and a membrane time constant z = 2.14 ms (PEARCE et al., 1982), the rheobasic field strength for the damped sine wave is approximately 50 V m-1. From Fig. 3, this corresponds to rheobase for a rectangular pulse of approximately 3 0 V m 1. This value is considerably greater than the 6 - 2 V m -1 selected from a survey of the literature for directly applied electrodes (REILLY, 1990). The reason for this apparent discrepancy warrants further investigation. We conclude that closed-chest magnetic stimulation of the heart is possible with a pulsed magnetic field, and the response is the same as that produced by direct electrical stimulation. From this study, it is now possible to establish the margin of safety for devices that use pulsed magnetic fields, such as peripheral nerve stimulators and magnetic resonance image (MRI) scanners. References AYERS, G. M., ARONSON,S. W. and GEDDES, L. A. (1986) Comparison of the ability of the Lapicque and exponential strength-duration curves to fit experimentally obtained data. Australasian J. Phy. Eng. Med., 9, (3), 111-116. BARKER, A. Z., JALINOUS, R. and FREESTON, I. L. (1985) Noninvasive magnetic stimluation of the human motor cortex. Lancet, l, 1106 1107. BARKER, A. T., EREESTON,I. L., JAL1NOUS,R. and JARRATT,J. A. (1987) Magnetic stimulation of the human brain and periphey'al nervous system: an introduction and the results of an initial clinical evaluation. Neurosurg., 20, (1), 100 109. BICKEORD, R. G. and FREMMING,B. D. (1965) Neural stimulation by pulsed magnetic fields in animals and man. 6th Int. Conf. Med. Elect. Biol. Eng. Tokyo, paper 7-6. BLAIR, H. A. (1932). On the intensity-time relations for stimulation by electric currents I. J. Gen. Physio., 15, 709 729. BOURLAND, J. D., TACKER, W. A. and GEDDES, L. A. (1978a) Strength-duration curves for trapezoidal waveforms of various tilts for transchest defibrillation in animals. Med. Instr., 12, 38-41. Medical & Biological Engineering & Computing
BOURLAND,J. D., TACKER,W. A., GEDDES, L. A. and CHAFFEE,V. (1978b) Comparative efficacy of damped sine wave and square wave current for transchest ventricular defibrillation in animals. Med. Instr., 12, 42-45. BOURLAND,J. D., MOUCHAWAR,G. A., NYENHUIS,J. A., GEDDES, L. A., FOSTER, K. S., JONES, J. T. and GRABER, G. P. (1990) Transchest magnetic (eddy-current) stimulation of the dog heart. Med. & Biol. Eng. & Comput., 28, 196-198. D'ARSONVAL,A. (1896). Dispositifs pour la measure des courants alternatifs des toutes frequences. C. R. Soc. Biol., 2, 450-451. GEODES, L. A. and BOURLAND,J. D. (1985) Tissue stimulation: theoretical considerations and practical applications. Med. & Biol. Eng. & Comput., 23, (2), 131 137. GEDDES, L. A. (1989) The history of stimulation with eddy currents due to time-varying magnetic yields. In Magnetic stimulation in clinical neurophysiology. CHOKROVERTY, S. (Ed.) Butterworths, Boston, MA, USA. GEDDES, L. A. and BAKER, L. E. (1989) In Principles of applied biomedical instrumentation, Third Edn., Wiley, New York, NY, USA. IRWIN, D. D., RUSHI S., EVERING, R., LEPESCHKIN,E., MONTGOMERY, D. B. and WEGGEL, R. J. (1970) Stimulation of cardiac muscle by a time-varying magnetic field. IEEE Trans., MAG-6, 321-322. LAPICQUE, L. (1909) Definition experimentale de l'excitation. Comptes Rendus Acad. Sci., 67, (2), 280-285. LAPICQUE,L. (1926) L'excitabilite enfonction du temps., Libraire J. Gilbert, Paris, MOUCHAWAR, G. A., GEDDES, L. A., BOURLAND, J. D. and PEARCE,J. A. (1989) Ability of the Lapicque and Blair strengthduration curves to fit experimentally obtained data from the dog heart. IEEE Trans., BME-36, (9), 971-974. NYENHUIS, J. A., MOUCHAWAR, G. A., BOURLAND, J. D. and GEDDES, L. A. (1991) Energy consideration on the magnetic (eddy-current) stimulation of tissues. IEEE Trans., MAG-27, (1), 680-687. PEARCE, J. A., BOURLAND,J. U., NEILSEN,W., GEDDES, L. A. and VOELZ, M. (1982) Myocardial stimulation with ultrashort duration current pulses. Pace, 5, 52-58. POLSON, M. J. R., BARKER, A. T. and FREESTON, I. L. (1982) Stimulation of nerve trunks with time-varying magnetic fields. Med. & Biol. Eng, & Comput., 20, 243-244. REILLY, J. P. (1990) Peripheral nerve and cardiac excitation by time-varying magnetic fields: a comparison of thresholds. Report MT 90 100, Office for Science and Technology, Center for Devices and Radiological Health, Food and Drug Administration, 12721 Twinbrook Parkway, Rockville, MD 20857. RENTSCH, W. (1965) The application of stimulation current with magnetic inductive energy. Dig. Fourth Int. Conf. Med. Elect. Biol. Eng., Tokyo, 109 111. SILNY, J. (1985) Effects of low-frequency, high intensity magnetic field on the organism. IEE Int. Conf. on Electric and Magnet. Fields in Medicine and Biology, 103-105. UENO, S., TASHIRO, T. and HARADA, K. (1988). Localized stimulation of neural tissues in the brain by means of a paired configuration of time-varying magnetic fields. J. Appl. Phys., 64, 5802--5804. WESSALE,J. L., BOURLAND,J. D., TACKER, W. A. and GEDDES, L. A. (1980) Bipolar catheter defibrillation in dogs using trapezoidal waveforms of various tilts. J. Electrocardiol. 13, (4), 359366.
Authors" biographies Gabriel A. Mouchawar was born in Aleppo, Syria, in 1964. He received the BS degree in Electrical and Computer Engineering (Summa Cum Laude) from Northeastern University, Boston, MA, in 1986 and the MS degree in electrical engineering from Purdue University, West Lafayette, IN, in 1987. He is currently working toward the Ph.D. degree in Electrical Engineering at the Hillenbrand Biomedical Engineering Center, Purdue University. His research interests include tissue stimulation and electromagnetics.
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Joe D. Bourland received a BA in Science/ Engineering and a BS in Electrical Engineering from Rice University and Ph.D. in Physiology from Baylor College of Medicine in Houston, Texas. He is co-ordinator for engineering at the Hillenbrand Biomedical Engineering Center. His research interests include the interaction of magnetic fields with living tissue, ventricular fibrillation/ defibrillation, electrophysiology and biomedical instrumentation. He is author of more than 100 publications in these areas and holds several patents. John A. Nyenhuis was born in the Netherlands in 1953. He received the BS degree in Physics from Indiana University, Bloomington, Indiana, USA. He received the MS degree in materials engineering and a Ph.D. degree in Electrical Engineering from Purdue University, West Lafayette, Indiana, USA. He is Associate Professor of Electrical Engineering at Purdue University. He is a Senior Member of the IEEE and a Full Member of the Bioelectromagnetics Society. His research interests are in magnetic materials and measurements, magnetic eddy-current stimulation and electromagnetic calculations. Leslie A. Geddes is the Showalter Distinguished Professor Emeritus of Bioengineering at Purdue University. Born in Scotland and educated in Canada, Dr Geddes holds the Bachelor's and Master's degrees in Electrical Engineering from McGill University (Montreal, Quebec, Canada) and the Ph.D. degree in Physiology from Baylor University College of Medicine, (Houston, Texas). He was awarded a D.Sc. Honoris Causea by McGill in 1971. While at
168
McGill, he was an instructor in Electrical Engineering and in neurophysiology. While at Baylor, he was Assistant, Associate, and Full Professor of Physiology and Director of the Division of Biomedical Engineering. Kirk S. Foster received a BS in Electrical Engineering in 1976 from Purdue University. He has been Senior Research Engineer at the Hillenbrand Biomedical Engineering Center since 1979 and is responsible for design and fabrication of equipment to support research in cardiac pacing, defibrillation, electrosurgery and casualty monitoring on the modern battle field. Outside interests include electronic music and auto racing. James T. Jones received an Associates Degree (1976) and the Bachelor Degree (1979) in Electrical Technology from Purdue University. He serves as the engineering manager for the Hillenbrand Biomedical Engineering center, which he joined in 1976. He is responsible for the design and fabrication of instruments used in research. He has designed and built a number of special-purpose computing systems which incorporate microprocessors. His hobbies include electronic music, computers and photography. George P. Graber was born in Louisville, KY, and received his BS in Electrical Engineering Technology from Purdue University. A research engineer, he has design expertise in the areas of medical electronics, high-energy equipment and microprocessor-based instrumentation.
Medical & Biological Engineering & Computing
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9 IFMBE: 1992
162
therapeutic devices employing magnetic fields to stimulate the heart without undue pain are contemplated. In a technical note, we (BoURLAND et al., 1990) reported excitation of the canine heart with a pulsed magnetic field produced by discharging a capacitor bank into a coil placed on the chest. The present l 1-dog study reports the threshold excitation-coil current and energy and the induced electric field strength required to excite the canine ventricles with two coplanar coils applied to the chest. 2 Theory 2.1 Conventional stimulation For excitable tissue to be stimulated, it is necessary to remove a critical amount of charge from the cell membrane. Removal of this charge reduces the resting membrane potential (RMP) by AV to the threshold potential (TP), at which point a regenerative process occurs with an opening of ion channels and a transmembrane movement of sodium and potassium ions, thereby generating an action potential. This process is illustrated for the cardiac muscle by the inset in Fig. 1. To achieve the initial reduction in transmembrane potential (AV), the stimulating current must establish a critical current density at the cell membrane for a finite time. The excitability characteristic of a tissue is described by the strength/duration curve, which is a plot of the threshold current against the pulse duration, d. There are two expressions for the strength/duration curve: the empirical LAPICQUE (1909; 1926) and the BLAIR (1932), which was derived using membrane theory. AVERS et al. (1986) and MOUCHAWAR et al. 0989) have shown that experimentally
M e d i c a l & Biological Engineering & Computing
March 1992
obtained data fit both expressions reasonably well. As the Blair expression was derived using the properties of the cell membrane, it will be used in the present study. However, the c o m m o n feature of both strength/duration expressions is that the shorter the duration of the current pulse, the higher the current required for stimulation. Fig. 1 shows strength/duration curves for the m o t o r nerve,
electric charge and A is the magnetic vector potential, the source of which is electric current (moving electric charge). In magnetic stimulation, the current in the excitation coil gives rise to an induced current density in the tissue. The electrical skin depth is 6, given by
1 =
(3)
2000l~
1~176176 \
\
200L -,,, \ -
where f is the frequency, /~ is the magnetic permeability and a is the tissue conductivity 9 Skin depth is a measure of the distance over which the applied AC magnetic field is attenuated by the induced eddy current. A typical equivalent frequency in magnetic stimulation is 10kHz, the permeability of tissue is nearly equal to the free space value of 4n x 10 7 H m - X and the conductivity is approximately 1 S m - 1. Therefore, the skin depth in the tissue is
0
100-. \,, ~ "'.. "\\ ~ j 50 -'".. \Xx ~ "'... "X ~ Jb 20 "'"-. "'x ~ \\ \ -
TP _ _~_]__ __\ RMP~ M..._.. stimulus
-Nd~
9.,.,,
I0
.... \\x\ "% "".,. ,,. \XX\ ~
5
0
0'001
L
0'01
1 (~tlssue
,
a
0.1
I
I
'0
'
I00
duration,ms
Fig. 1 Strength/duration curves for motor nerve, sensory receptors and cardiac muscle. For ease of comparison, the curves have been normalised to the same rheobase. Inset shows the mechanism of stimulation. [ T P = threshold potential, R M P = resting membrane potential, d = duration, (J/Jb) = (1/1 e-a/~)] heart z = 2 ms sensory receptors z = 0"5 ms ....... motor nerve z = 0.1 ms -
=
~/(~)(lO*)(4~z x 10-7)(1)
=
5m
Typically, the distance between the coil and the target tissue is a few cm, much less than 6ti.... . Consequently, the contribution of the eddy-current in the tissue to the induced electric field can be neglected in calculating the vector potential. At a point r in the tissue, the vector potential A is obtained by integrating over the current in the coil A(r) =
/to f Jcoit(r') d V '
(4)
-
sensory receptors and cardiac muscle. The current is represented as current density J divided by the rheobasic current, density Jb- The rheobase is the long-duration current asymptote. The Blair expression for the strength/duration curve in terms of current density J is Jb J - (1 - e -d/r (1) where Jb is the rheobase and z is the membrane time constant, a quantity that is specific for each type of tissue; z is also temperature dependent (GEDDES and BOURLAND, 1985). The membrane time constant is the duration for which J / J b = 1"58. Fig. 1 shows that with a stimulus of 0.1 ms, the threshold for stimulating the m o t o r nerve (z --~ 0.1 ms) is 1.58 Jb" However, if the same pulse duration is used to stimulate the heart (z ~ 2 ms), the current density must be 20-5 times the rheobase or 13 times that required to stimulate the m o t o r nerve. Therefore, for stimulating cardiac muscle, a longer pulse duration is desirable. With a rectangular pulse, the average rheobasic current density for cardiac muscle is 1 . 4 8 m A c m 1 (PEARCE et al., 1982) and the resistivity is approximately 4 0 0 D c m (GEDDES and BAKER, 1989). Therefore, the expected rheobasic electric field strength is E b = PJb = 5 9 2 m V c m 1 ~ 6 0 V m - ~ . 2.2 Eddy-current stimulation With magnetic (eddy-current) stimulation, the induced electric field E causes current to flow in the tissue, thereby causing stimulation. The current density J is E/p, where p is the resistivity of the tissue. In a stationary system, the electric field E is given by OA E = - - V ( I ) - c~--t-
(2)
where (I) is the electrostatic potential that arises from fixed Medical & Biological Engineering & C o m p u t i n g
where 2cou(r' ) is the current density at point r' in the coil, /~o is the permeability of free space and dV' is an element of volume. The electrostatic potential at point r is given by
*(,.)
=
["
4Xeo J Ir - r'l
dV'
(5)
where r is the electric charge density at point r', eo is the permittivity of free space, dV' is an element of volume and the integral is taken over all space. It can be shown using Maxwell's equations that there is no electric charge due to a time-varying electric field within a linear dielectric of uniform electrical properties. The primary origin of V~ in magnetic stimulation is the electrical charges that accumulate at the interfaces between regions of different conductivity in the tissue and at the air/skin interface of the subject. For typical tissues and stimulation waveforms, the dielectric relaxation time e/a is small compared to the period of the stimulating current pulse. The charges at the interface can then be calculated from the resulting requirement that the normal component of the current density is continuous at an interface between different conductors. 2.3 Predicted energy f o r cardiac stimulation Using the Blair expression we can demonstrate how the energy delivered to the coils varies with pulse duration for stimulation with a pulsed magnetic field. With the electric field E = p J as the stimulus, the Blair expression is Eb
E--(l_e
d/,)
(6)
where Eb is the rheobasic electric field and ~ is the membrane time constant. The induced electric field E is proportional to the first time derivative of the coil current di/dt. To generate an idealised rectangular pulse of electrical field E in the tissue, the current in the coil must be a rising r a m p with a constant time derivative of K E , where
M a r c h 1992
163
K is a constant of proportionality that depends on coil geometry and coil-to-tissue distance. The peak magnetic field energy UB delivered to the coils is given by 1 2 UB = -iLIp
(7)
where L is the coil inductance and Ip is the peak current in the coil. If the ramp is used for the coil current waveform, Ip is equal to KEd, where d is the duration to the peak of the current ramp (and is also the duration of the induced rectangular electric field pulse). Therefore, K2 U . = - ~ L(Ed) 2
(8)
Substituting the expression for E from the strength/ duration curve into the preceding equation we obtain Kz E~ UB = -~- L (1 -- e-d/q 2 d2
(9)
For the simple geometry of small coils parallel to the tissue surface, the tissue can be modelled as an infinite conductive half-space. For this case, the constant K can be shown to be numerically equal to 1/A o, where A 0 is the magnitude of the magnetic vector potential (eqn. 4) evaluated at the target tissue depth for 1 A of current in the stimulating coil assembly (NYENHU]S et al., 1991). The value of A 0, obtained from a computer model of the two-coil assembly used for cardiac stimulation, was 7-6 • 10 -6 V s A - 1 m - ~. Evaluating A o by computer simulation for a coil-to-tissue distance of 2-5cm and for the coils shown in Fig. 2, the predicted magnetic field energy against pulse duration required to stimulate the dog heart (z ~ 2 ms) can be calculated as a function of pulse duration. As shown in Fig. 2, the magnetic field energy decreases monotonically as duration decreases. The magnetic field energy approaches a minimum asymptotically as the duration of the pulse approaches zero. To find the minimum, we can use the Taylor series expansion for the exponential e -d/~. Neglecting the higher-than-linear terms, the expansion becomes 1 - (d/z), for d ~ z. The minimum energy is therefore L
L E~ dZ = ~ o
(10)
E~z 2
If we use J b = 1.48mAcro 2 and p = 4 0 0 f 2 c m , the expected rheobasic electric field strength is E b ~ 60 V m-~ and the minimum predicted energy for cardiac stimulation is U~,~.--27kJ. As a practical matter, the rapid rate of flux change required for minimum energy stimulation exceeds the practical construction technique and electronic 200
_~ 16o
device specifications, and so a compromise between minimum energy and device limitations must be achieved. Based on our experience with high-energy defibrillators designed and constructed for research, we chose to limit the capacitor-bank voltage to 10000V; the predicted threshold energy is approximately 36 kJ and the duration of the generated pulse is approximately 600/zs. The magnetic stimulator used in this study was designed to induced a 571/zs pulse in the tissue. 2.4 Magnetically-induced stimulus waveform As shown in Section 2.3, the energy required for magnetic stimulation of the heart is large. A typical magnetic stimulator includes an energy-storage capacitor, which is discharged into an excitation coil. F r o m Faraday's law of induction, the waveform of the current density (J) induced in the tissue is proportional to the first time derivative (dic/dt) of the current (ic) in the excitation coil. WESSALEet al. (1980) and BOURLAND et al. (1978a; b) have shown that trapezoidal and damped sine waves are equally effective if they have the same average current. This provides a convenient way to relate the peak value of the induced field to its efficacy. (The peak and average values are the same for a rectangular pulse.) When a capacitor C, charged to V V, is discharged into an excitation coil of inductance L and circuit resistance R, the current in the coil is a damped sinusoid. With a typical magnetic stimulator, the damping D = (R/2)x/(C/L) is less than 1.0 and the excitation coil current (ic) waveform is oscillatory and is given by V i~ = - ~ e -~t sin cot
(11)
where ~ = R / 2 L and co = x / ( 1 / L C ) - ~2 (GEDDES and BAKER, 1989). A resistor and series diode were placed in parallel with the energy-storage capacitors of the generator used in this study to prevent significant reverse voltage developing across the (electrolytic) energy-storage capacitors. A similar circuit configuration was used by BARKER et al. (1985). The resistor-diode network increases the decay time constant after the peak in coil current and the reverse current density induced in the tissue is attenuated and prolonged. Consequently, stimulation is caused by the portion of the waveform from the time of onset (t = 0) to the time of peak coil current (t = Zp). (The diode of the added circuitry is reverse-biased during this time, 0 ~< t ~< zp, and the additional circuitry has no effect on the coil current and the induced current density.) Let F be the ratio of the average induced current density (Jav) to peak induced current density (Je) in the time 0 ~< t ~< rp, i.e. I" = (JAv/Jp). Assuming that the tissue is a linear conductor, the induced current density is proportional to the first time derivative of the coil current. Noting also that the peak of the induced current occurs at t -- 0, then
o
120
F = zv J~ ._u
dt dt =
ic(t = Zv)
dic (t = O)
80
di~
at
O
(t
(12)
= o)
Using the preceding expressions for i~ and noting that (di~/dt) (t = O)= (V/L), we obtain the following for the underdamped circuit. 0 I
o.oi
' o.1o
' 1.oo
1o.'0 o
Underdamped case: D < 1
durolion.ms Fig. 2
164
Predicted energy required against stimulus duration for stimulating cardiac muscle with a pulsed magnetic field
z,
=
-- tan-1 fO
=
-- tan-1 fO
Medical & Biological Engineering & Computing
(13) March 1992
where 7 = ~/o9 = (D/~/1 - D 2 ) . The average-to-peak ratio for the induced current can be calculated as a function of damping from e - ' 'a"-'(1/y) sin ( t a n - 1 ~) F =
(14) tan- 1 1 7
and Welfare (DHHS publication NIH 85-23, revised 1985). In addition, this study was approved by the Purdue University Animal Care and Use Committee. Ectopic beats were produced in the vagal-arrested hearts of 11 male and female mongrel dogs, with body weights from 17 to 26kgl The dogs were anaesthetised with IV pentobarbital sodium (30mgkg-l), intubated, ventilated with room air and placed in left lateral recumbency. The coplanar coils were placed beneath the dog, with the heart
Similarly, the following expressions for F in the critically damped (D = 1.0) and overdamped cases (D > 1.0) can be obtained. Critically damped case: D = 1 F-
1 (15)
e
o 8.5cm
Overdamped case: D > 1
expl--89 F=
-- 1) In 7 + 11] - exp[- 89 7-7+1 In m 7-1
+ 1) In 7 + 11] Y-
(16)
~
~ B1
where D
,
L
~
~~
~
.
~
~
1.25cm
7 -- , , / D 2 _ 1 "
Fig. 3 shows the ratio of the average-to-peak induced current against the damping coefficient (D) for the range 0-1.5. This illustration shows that it is desirable to select a
01
I
lay
o, O.
r-
04,
0.2
o
o'.5
~io
1!5
damping,D
Fig. 3
Fig. 4
(a) Position o f the coplanar coils (broken circles) under the left side o f the dog; (b) dimensions and current f l o w in the coils
above the point where the perimeters of the coils touched, as shown in Fig. 4. Lead II electrocardiogram and the direct arterial pressure were recorded. A bipolar stimulating electrode was placed inside an insulating sleeve and in contact with the right vagus nerve in the neck. Reversible and temporary cardiac arrest was achieved by stimulating the right vagus nerve with a train of rectangular pulses, 0.1 ms in duration at 50s 1 and approximately 15 V, using a Grass $44 stimulator and SIU5 isolation unit (Grass Instrumentations, Quincy, MA, USA). Prior to delivering magnetic pulses, and at selected times throughout the procedure, the vagus nerve was stimulated and magnetic pulses were not delivered to verify that latent cardiac pacemakers were silent.
Ip
0.8
B2
Ratio F of the average-to-peak value of induced current/ density pulse in the time between the onset (t = O) of the pulse and the time (t = zp) of the zero crossing of the pulse as a function of damping D
low damping to obtain a high average current. The damping coefficient for the stimulator used in this study was D = 0.105, and the peak induced field can be related to that for a rectangular pulse by multiplying by 0.581. 3 M e t h o d s and m a t e r i a l s
3.1 Animal preparation All experiments were performed in accordance with the Guide for the Care and Use of Laboratory Animals, published by the US Department of Health, Education Medical & Biological Engineering & Computing
3.2 Excitation coils Two coplanar coils (Fig. 4) provided the pulsed magnetic field. This arrangement concentrates the induced electrical field in the region where the coils are adjacent when the coils are connected so that current flows in the same direction at the point of contact (Fig. 4b) (UENO et al., 1988). NYENHUIS et al. (1991) have shown that the use of two coplanar coils, instead of one coil of the same dimensions, results in the reduction of almost a factor of two in the energy required to achieve stimulation. Each coil consisted of 30 turns of 0.5in x 0.043in of copper ribbon covered with braided glass sleeving and sealed with epoxy cement. The inner and outer diameters of each coil were 7 and 17cm, respectively. The coils were mounted with their edges touching. This geometry provides optimum stimulation of a target 2.5 cm from the adjacent coil edges (NYENHUIS e t al., 1991). The distance between the plane of the coil and the heart
March 1992
165
was measured by inserting the hypodermic needle through the intercostal space where the coils touched. The needle was advanced until cardiac motion was felt through the needle, or until ectopic beats were provoked by the sharp needle point. In these studies the distance from the coils to the ventricles within the chest ranged from 2 to 3-5 cm. 3.3 Magnetic stimulator A simplified equivalent circuit of the magnetic stimulator and coils is a series R C L circuit, comprising a 682 #F 9 9 0 0 V capacitor, an output switch (ignitron) and a 220 m H inductor (combined value for both coils, including mutual inductance). In addition, a 220ml) resistance and reverse-biase diode is connected across the 682#F capacitor to prevent reverse polarisation. A similar circuit was described by BARKER et al. (1985) for stimulation of the h u m a n brain. Delivery of the current was initiated by triggering a General Electric GL7171 ignitron. The equivalent internal series resistance of the generator is approximately
3
vagal stimulation
"o
0
0
2
4
6
8
10
time,s G -1-
85 m~); the series resistance of the two coils and connecting leads is approximately 35 m~). The generator specifications are: m a x i m u m voltage 9900V, m a x i m u m peak current 17000A and maximum stored energy 33 400J. Surge line current was limited to 13 A (at 115 V) so that the magnetic stimulator could be powered from any standard outlet in the laboratory; maximum line current is required only during charging of the energy-storage capacitors. Full charge is achieved in approximately 90 s. The waveform of the electric field induced in the tissue by the magnetic stimulator used in this study is shown in the inset of Fig. 3. The damping D = 0-105 and the duration to the first zero crossing of the induced current is zp = 571#s. 3.4 Threshold stimulus determination The procedure used to determine the threshold current and energy required to evoke a cardiac contraction was as follows: The capacitor bank was charged to a selected voltage. The right vagus nerve was stimulated to temporarily arrest the heart. After sufficient time to verify cardiac arrest, typically about 3 s, a test pulse was delivered while monitoring the ECG and blood pressure recordings. If an ectopic beat was produced, the capacitor-bank voltage was reduced by decrements of l0 per cent until the pulsed magnetic field failed to evoke a ventricular contraction. Otherwise, the capacitor-bank voltage was increased by increments of 10 per cent until an ectopic beat was produced. The threshold was defined as that voltage (and current) for which 10 per cent less did not stimulate. For each trial, the heart was arrested for about 5s. The procedure was repeated to obtain a threshold with current flowing in the opposite direction in the pair of coils.
E 200
E :3
160
& ~20 13 0
o
80
.13
~L.
40
mognetic pulse delivered
l
L, 0
i
i
2
4
i
i
6
8
time, s b
Fig. 5
(a) ECG; (b) blood pressure, before cardiac arrest, during cardiac arrest of the heart and after cessation of vagal stimulation. During cardiac arrest the magnetic stimulator evoked an ectopic beat, shown by the QS-wave and the blood-pressure pulse P Table 1
166
4 Results Fig. 5 is a typical recording of the E C G and blood pressure prior to cardiac arrest, during arrest with vagal stimulation when an ectopic beat was induced by the magnetic stimulator and following cessation of vagal stimulation when the heart resumed normal sinus rhythm. Note that during the period of cardiac arrest, the ectopic beat induced by the pulsed magnetic field provided an inverted (QS) waveform in the ECG, indicating apical stimulation of the ventricles. The mean threshold stimulating current in the excitation coils was about 9250A. Table 1 presents the threshold peak currents and energies for current flow in directions A and B. Direction A was defined as anticlockwise current in the cranial coil and clockwise in the caudal coil, when
Threshold current and energy delivery to the excitation coil
Dog number
Current Direction A (A)
Current Direction B (A)
Stored energy Direction A (J)
Stored energy Direction B (J)
Average stored energy (J)
Energy ratio A/B
Induced E field Vm '
1 2 3 4 5 6 7 8 9 10 11
8600 9200 8000 8800 9400 8800 10000 10200 9600 10600 8800
8500 10200 8800 8000 9400 8800 10000 9400 9200 9400 9600
9385 12258 8513 10300 12258 10300 14386 14386 12258 15285 11454
9385 14386 10300 8513 12258 10300 14386 12258 12258 12258 13514
9385 13322 9407 9407 12258 10300 14386 13322 12258 13772 12484
1.0 0.85 0-83 1.21 1.0 1.0 1.0 1.17 1.0 1.25 0-85
213 230 227 207 182 205 212 216 196 216 237
Mean SD
9273 776
9209 646
11889 2175
11801 1957
11846 1887
1.01 0-14
213 16
M e d i c a l & Biological Engineering & C o m p u t i n g
M a r c h 1992
viewed from above. Direction B is the reverse. The average threshold for inducing an ectopic beat was slightly greater with current flow in direction A than B, but the difference was not significant at p = 0.05.
5 Discussion In this paper, we have presented both theoretical predictions and experimental data for cardiac threshold. The theoretical predictions were based on a simplified model of the experimental subject, and were not expected to be in quantitative agreement with the experimentally determined values for cardiac threshold, but rather, were used to optimise the design of the hardware. We anticipated, as had others, that the energy required for cardiac stimulation would be considerable, and we desired to reduce the size and power of the pulse generator as much as possible, by optimising the design for minimum energy. An average energy of approximately 12kJ was required to achieve closed-chest magnetically induced ectopic beats in the 17-26 kg dogs. The energy required to stimulate the heart is much greater than that reported for superficial motor nerves (BICKFORD and FREMMING, 1965; POLSON et al., 1982), but is considerably less than the 20-105kJ suggested by IRWIN et al. (1970). The energy required to stimulate the heart is more than an order of magnitude higher than the energy required to stimulate the human brain and peripheral nervous system (typically 400 J). If it is assumed that the charge accumulated at boundaries between tissues with differing resistivity is insignificant, the mean peak induced electric field for threshold stimulation in the dog was 2 1 3 V m -1 for the 571kts damped sine wave pulse. Using the Blair expression and a membrane time constant z = 2.14 ms (PEARCE et al., 1982), the rheobasic field strength for the damped sine wave is approximately 50 V m-1. From Fig. 3, this corresponds to rheobase for a rectangular pulse of approximately 3 0 V m 1. This value is considerably greater than the 6 - 2 V m -1 selected from a survey of the literature for directly applied electrodes (REILLY, 1990). The reason for this apparent discrepancy warrants further investigation. We conclude that closed-chest magnetic stimulation of the heart is possible with a pulsed magnetic field, and the response is the same as that produced by direct electrical stimulation. From this study, it is now possible to establish the margin of safety for devices that use pulsed magnetic fields, such as peripheral nerve stimulators and magnetic resonance image (MRI) scanners. References AYERS, G. M., ARONSON,S. W. and GEDDES, L. A. (1986) Comparison of the ability of the Lapicque and exponential strength-duration curves to fit experimentally obtained data. Australasian J. Phy. Eng. Med., 9, (3), 111-116. BARKER, A. Z., JALINOUS, R. and FREESTON, I. L. (1985) Noninvasive magnetic stimluation of the human motor cortex. Lancet, l, 1106 1107. BARKER, A. T., EREESTON,I. L., JAL1NOUS,R. and JARRATT,J. A. (1987) Magnetic stimulation of the human brain and periphey'al nervous system: an introduction and the results of an initial clinical evaluation. Neurosurg., 20, (1), 100 109. BICKEORD, R. G. and FREMMING,B. D. (1965) Neural stimulation by pulsed magnetic fields in animals and man. 6th Int. Conf. Med. Elect. Biol. Eng. Tokyo, paper 7-6. BLAIR, H. A. (1932). On the intensity-time relations for stimulation by electric currents I. J. Gen. Physio., 15, 709 729. BOURLAND, J. D., TACKER, W. A. and GEDDES, L. A. (1978a) Strength-duration curves for trapezoidal waveforms of various tilts for transchest defibrillation in animals. Med. Instr., 12, 38-41. Medical & Biological Engineering & Computing
BOURLAND,J. D., TACKER,W. A., GEDDES, L. A. and CHAFFEE,V. (1978b) Comparative efficacy of damped sine wave and square wave current for transchest ventricular defibrillation in animals. Med. Instr., 12, 42-45. BOURLAND,J. D., MOUCHAWAR,G. A., NYENHUIS,J. A., GEDDES, L. A., FOSTER, K. S., JONES, J. T. and GRABER, G. P. (1990) Transchest magnetic (eddy-current) stimulation of the dog heart. Med. & Biol. Eng. & Comput., 28, 196-198. D'ARSONVAL,A. (1896). Dispositifs pour la measure des courants alternatifs des toutes frequences. C. R. Soc. Biol., 2, 450-451. GEODES, L. A. and BOURLAND,J. D. (1985) Tissue stimulation: theoretical considerations and practical applications. Med. & Biol. Eng. & Comput., 23, (2), 131 137. GEDDES, L. A. (1989) The history of stimulation with eddy currents due to time-varying magnetic yields. In Magnetic stimulation in clinical neurophysiology. CHOKROVERTY, S. (Ed.) Butterworths, Boston, MA, USA. GEDDES, L. A. and BAKER, L. E. (1989) In Principles of applied biomedical instrumentation, Third Edn., Wiley, New York, NY, USA. IRWIN, D. D., RUSHI S., EVERING, R., LEPESCHKIN,E., MONTGOMERY, D. B. and WEGGEL, R. J. (1970) Stimulation of cardiac muscle by a time-varying magnetic field. IEEE Trans., MAG-6, 321-322. LAPICQUE, L. (1909) Definition experimentale de l'excitation. Comptes Rendus Acad. Sci., 67, (2), 280-285. LAPICQUE,L. (1926) L'excitabilite enfonction du temps., Libraire J. Gilbert, Paris, MOUCHAWAR, G. A., GEDDES, L. A., BOURLAND, J. D. and PEARCE,J. A. (1989) Ability of the Lapicque and Blair strengthduration curves to fit experimentally obtained data from the dog heart. IEEE Trans., BME-36, (9), 971-974. NYENHUIS, J. A., MOUCHAWAR, G. A., BOURLAND, J. D. and GEDDES, L. A. (1991) Energy consideration on the magnetic (eddy-current) stimulation of tissues. IEEE Trans., MAG-27, (1), 680-687. PEARCE, J. A., BOURLAND,J. U., NEILSEN,W., GEDDES, L. A. and VOELZ, M. (1982) Myocardial stimulation with ultrashort duration current pulses. Pace, 5, 52-58. POLSON, M. J. R., BARKER, A. T. and FREESTON, I. L. (1982) Stimulation of nerve trunks with time-varying magnetic fields. Med. & Biol. Eng, & Comput., 20, 243-244. REILLY, J. P. (1990) Peripheral nerve and cardiac excitation by time-varying magnetic fields: a comparison of thresholds. Report MT 90 100, Office for Science and Technology, Center for Devices and Radiological Health, Food and Drug Administration, 12721 Twinbrook Parkway, Rockville, MD 20857. RENTSCH, W. (1965) The application of stimulation current with magnetic inductive energy. Dig. Fourth Int. Conf. Med. Elect. Biol. Eng., Tokyo, 109 111. SILNY, J. (1985) Effects of low-frequency, high intensity magnetic field on the organism. IEE Int. Conf. on Electric and Magnet. Fields in Medicine and Biology, 103-105. UENO, S., TASHIRO, T. and HARADA, K. (1988). Localized stimulation of neural tissues in the brain by means of a paired configuration of time-varying magnetic fields. J. Appl. Phys., 64, 5802--5804. WESSALE,J. L., BOURLAND,J. D., TACKER, W. A. and GEDDES, L. A. (1980) Bipolar catheter defibrillation in dogs using trapezoidal waveforms of various tilts. J. Electrocardiol. 13, (4), 359366.
Authors" biographies Gabriel A. Mouchawar was born in Aleppo, Syria, in 1964. He received the BS degree in Electrical and Computer Engineering (Summa Cum Laude) from Northeastern University, Boston, MA, in 1986 and the MS degree in electrical engineering from Purdue University, West Lafayette, IN, in 1987. He is currently working toward the Ph.D. degree in Electrical Engineering at the Hillenbrand Biomedical Engineering Center, Purdue University. His research interests include tissue stimulation and electromagnetics.
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Joe D. Bourland received a BA in Science/ Engineering and a BS in Electrical Engineering from Rice University and Ph.D. in Physiology from Baylor College of Medicine in Houston, Texas. He is co-ordinator for engineering at the Hillenbrand Biomedical Engineering Center. His research interests include the interaction of magnetic fields with living tissue, ventricular fibrillation/ defibrillation, electrophysiology and biomedical instrumentation. He is author of more than 100 publications in these areas and holds several patents. John A. Nyenhuis was born in the Netherlands in 1953. He received the BS degree in Physics from Indiana University, Bloomington, Indiana, USA. He received the MS degree in materials engineering and a Ph.D. degree in Electrical Engineering from Purdue University, West Lafayette, Indiana, USA. He is Associate Professor of Electrical Engineering at Purdue University. He is a Senior Member of the IEEE and a Full Member of the Bioelectromagnetics Society. His research interests are in magnetic materials and measurements, magnetic eddy-current stimulation and electromagnetic calculations. Leslie A. Geddes is the Showalter Distinguished Professor Emeritus of Bioengineering at Purdue University. Born in Scotland and educated in Canada, Dr Geddes holds the Bachelor's and Master's degrees in Electrical Engineering from McGill University (Montreal, Quebec, Canada) and the Ph.D. degree in Physiology from Baylor University College of Medicine, (Houston, Texas). He was awarded a D.Sc. Honoris Causea by McGill in 1971. While at
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McGill, he was an instructor in Electrical Engineering and in neurophysiology. While at Baylor, he was Assistant, Associate, and Full Professor of Physiology and Director of the Division of Biomedical Engineering. Kirk S. Foster received a BS in Electrical Engineering in 1976 from Purdue University. He has been Senior Research Engineer at the Hillenbrand Biomedical Engineering Center since 1979 and is responsible for design and fabrication of equipment to support research in cardiac pacing, defibrillation, electrosurgery and casualty monitoring on the modern battle field. Outside interests include electronic music and auto racing. James T. Jones received an Associates Degree (1976) and the Bachelor Degree (1979) in Electrical Technology from Purdue University. He serves as the engineering manager for the Hillenbrand Biomedical Engineering center, which he joined in 1976. He is responsible for the design and fabrication of instruments used in research. He has designed and built a number of special-purpose computing systems which incorporate microprocessors. His hobbies include electronic music, computers and photography. George P. Graber was born in Louisville, KY, and received his BS in Electrical Engineering Technology from Purdue University. A research engineer, he has design expertise in the areas of medical electronics, high-energy equipment and microprocessor-based instrumentation.
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